Apparent Michaelis constant of the enzyme modified porous electrode

Abstract

Plate-gap model of enzyme doped porous electrode was utilized in order to calculate apparent Michaelis constants ( $$K_{\rm M}^{\rm app}$$ ) and apparent maximal currents ( $$I_{\rm max}^{\rm app}$$ ) of modeled amperometric biosensor for the wide range of given reaction/diffusion parameters. It was found that $$K_{\rm M}^{\rm app}$$ of plate-gap biosensor linearly depends on $$I_{\rm max}^{\rm app}$$ when rates of enzymatic reaction are lower than critical. Theoretically predicted linear correlation between apparent parameters was observed experimentally for the case of carbon paste electrodes, which were modified by PQQ-dependent alcohol dehydrogenases. At overcritical rates (or apparent maximal currents), $$K_{\rm M}^{\rm app }$$ is practically independent on Michaelis constant of soluble enzyme. Therefore, apparent Michaelis constant can be regarded as biosensor’s topology representing parameter which, in fact, is not related to the specificity of enzyme kinetics. High and rate-independent values of $$K_{\rm M}^{\rm app}$$ indicate that reaction proceeds at substrate-exposed top layer of the gap. In this case, reaction–diffusion system formally is stratified into separate reaction (top) and diffusion (bottom) zones. Topology of such reaction–diffusion system reminds “inverted” planar electrode, which contains diffusion layer below reaction layer. The net effect of plate-gap topology of working electrode on apparent Michaelis constant is similar to the effect of diffusion layer covering enzymatic planar electrode.